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Trambak Banerjee

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3 papers

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JMLR Journal 2021 Journal Article

A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family

Trambak Banerjee
Qiang Liu
Gourab Mukherjee
Wengunag Sun

We develop a Nonparametric Empirical Bayes (NEB) framework for compound estimation in the discrete linear exponential family, which includes a wide class of discrete distributions frequently arising from modern big data applications. We propose to directly estimate the Bayes shrinkage factor in the generalized Robbins' formula via solving a convex program, which is carefully developed based on a RKHS representation of the Stein's discrepancy measure. The new NEB estimation framework is flexible for incorporating various structural constraints into the data driven rule, and provides a unified approach to compound estimation with both regular and scaled squared error losses. We develop theory to show that the class of NEB estimators enjoys strong asymptotic properties. Comprehensive simulation studies as well as analyses of real data examples are carried out to demonstrate the superiority of the NEB estimator over competing methods. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

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JMLR Journal 2021 Journal Article

Improved Shrinkage Prediction under a Spiked Covariance Structure

Trambak Banerjee
Gourab Mukherjee
Debashis Paul

We develop a novel shrinkage rule for prediction in a high-dimensional non-exchangeable hierarchical Gaussian model with an unknown spiked covariance structure. We propose a family of priors for the mean parameter, governed by a power hyper-parameter, which encompasses independent to highly dependent scenarios. Corresponding to popular loss functions such as quadratic, generalized absolute, and Linex losses, these prior models induce a wide class of shrinkage predictors that involve quadratic forms of smooth functions of the unknown covariance. By using uniformly consistent estimators of these quadratic forms, we propose an efficient procedure for evaluating these predictors which outperforms factor model based direct plug-in approaches. We further improve our predictors by considering possible reduction in their variability through a novel coordinate-wise shrinkage policy that only uses covariance level information and can be adaptively tuned using the sample eigen structure. Finally, we extend our disaggregate model based methodology to prediction in aggregate models. We propose an easy-to-implement functional substitution method for predicting linearly aggregated targets and establish asymptotic optimality of our proposed procedure. We present simulation experiments as well as real data examples illustrating the efficacy of the proposed method. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

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NeurIPS Conference 2021 Conference Paper

Rethinking gradient sparsification as total error minimization

Atal Sahu
Aritra Dutta
Ahmed M. Abdelmoniem
Trambak Banerjee
Marco Canini
Panos Kalnis

Gradient compression is a widely-established remedy to tackle the communication bottleneck in distributed training of large deep neural networks (DNNs). Under the error-feedback framework, Top-$k$ sparsification, sometimes with $k$ as little as 0. 1% of the gradient size, enables training to the same model quality as the uncompressed case for a similar iteration count. From the optimization perspective, we find that Top-$k$ is the communication-optimal sparsifier given a per-iteration $k$ element budget. We argue that to further the benefits of gradient sparsification, especially for DNNs, a different perspective is necessary — one that moves from per-iteration optimality to consider optimality for the entire training. We identify that the total error — the sum of the compression errors for all iterations — encapsulates sparsification throughout training. Then, we propose a communication complexity model that minimizes the total error under a communication budget for the entire training. We find that the hard-threshold sparsifier, a variant of the Top-$k$ sparsifier with $k$ determined by a constant hard-threshold, is the optimal sparsifier for this model. Motivated by this, we provide convex and non-convex convergence analyses for the hard-threshold sparsifier with error-feedback. We show that hard-threshold has the same asymptotic convergence and linear speedup property as SGD in both the case, and unlike with Top-$k$ sparsifier, has no impact due to data-heterogeneity. Our diverse experiments on various DNNs and a logistic regression model demonstrate that the hard-threshold sparsifier is more communication-efficient than Top-$k$.

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